Acceleration of expanding universe question

[qedigiv]

If we are looking further and further back in time when we look at more and more distant galaxies, then how do we know that they are accelerating (instead of that they were accelerating a long long time ago)??

 

[mfb]

You can look at galaxies everywhere from "now" to ~13 billion years ago. This allows to get the current velocities as well as the velocities in the past.
You don't see the same galaxies as they are now and as they were 13 billion years ago, of course, but if you see the current velocity of galaxies nearby you can extrapolate this to get the current velocity of more distant galaxies.